I too had and repaired this nusence trouble with the HP Photosmart 7510 printer. Attached are pictures:
1. cut hole in bottom of printer below the "pickup roller gear set".
2. slide "slipping" gear off to side and clean with alchol.
3. apply epoxy to gear axis with long wooden q-tip (or similar tool), then reposition gear.
4. let dry and start printing.
[https://drive.google.com/file/d/1zg0QbE4Jm8F8FJc-zXdmdWIChHKxEGpFIg/view?ts=5aca4494]
[https://drive.google.com/file/d/1GjiEro_aSBdLzFMCRXFJ-8k3J2gSvbRAow/view?ts=5aca43e6]
Hope this helps.